Scenario 8 The Labor Contract at the Plant Prohibits Both Overtime and Manufacturing

Scenario 8.1 — Gang Aft Agley
Gang Aft Agley, a manufacturing company, faces the aggregate planning problem shown in the table below. Cost of regular production is $5 per unit, the cost of producing the same unit on overtime is $7.50, the cost of subcontracting is $9 per unit, and the cost of carrying a unit in inventory from one month to the next is $2.
$\begin{array}{|l|c|c|c|c|c|}\hline & \text { January } & \text { February } & \text { March } & \text { April } & \text { May } \\\hline \text { Forecast } & 500 & 750 & 1200 & 650 & 300 \\\hline \text { Beginning Inventory } & 100 & & & & \\\hline \text { Regular Time } & & & & & \\\hline \text { Overtime } & & & & & \\\hline \text { Subcontracting } & & & & & \\\hline \text { Ending Inventory } & & & & & \\\hline\end{array}$
The labor contract at the plant prohibits both overtime and subcontracting output to exceed 300 units in any five month window. The plant capacity is 600 units per month produced using two shifts, regardless of the number of days in a month. By policy, management wants to avoid stockouts.
-Formulate the aggregate plan using linear programming.